Kristen Wiig has had the kind of summer one might imagine to be life-changing. For four years, she andAnnie Mumolo, her friend and co-writer, slaved over a comedy script commissioned by Judd Apatow about a woman whose best friend is getting married. It was the 38-year-old's first lead in a film, and her first full-length script to be produced. As an indication of how it played with audiences, I watched it on a plane last month with a friend who, during the scene in which the bride squats in the street to relieve herself after a bad kebab, laughed so long and hard a woman passing in the aisle leant over and said, "What are you watching?"

Wiig smiles when I tell her this. "Proud," she says, of the day they filmed the shitting-in-the-street scene. "A proud moment."

We are in the tearoom of a fashionable hotel in Tribeca, the Manhattan neighbourhood where Wiig lives. Before Bridesmaids, she was known to US audiences as a long-running cast member of Saturday Night Live and elsewhere for scene-stealing cameos in films such as Ghost Town and Knocked Up.

That the film, by midsummer, had grossed more than $150m in the US and outstripped not only all of Apatow's other films, but every "R-rated female comedy" in history, puts Wiig in the zone of woman of the moment, although she chafes against this, with its implication that before Bridesmaids she was an ingenue.

"In most ways my life hasn't changed," she says. "I know that's a boring answer. People want to hear that I bought all gold, fur…" She allows a perfectly timed beat. "I would never wear fur."

But hasn't she had to turn down lots of offers?

"I mean. Yes, no. It feels weird to say that; you don't want to be like, 'Everyone wants me!' I mean. I guess Bridesmaids was definitely the biggest role I've ever had. And the fact that I co-wrote it and everything. But, um…" Wiig, who is slight, with very straight hair and an eager tilt to her body language, looks mortified. "It's not like I have boxes of scripts arriving at my door."

Her understatement is fuelled perhaps by the inevitable and awkward comparisons she has gained with other women in her business, as if the culture can sustain only a couple at a time. Wiig has been getting "the new Tina Fey" quite a lot – Fey was head writer at SNL when Wiig joined – although the comparison is faulty. Wiig is an actor first and a comedian second, and with a film directed by Sean Pennin the pipeline and another, Imogene, in which she stars alongside Annette Bening and Matt Dillon, wants to develop her career away from comedy. "People always call me a comedian. And I don't really see myself like that. I guess I just consider myself an actor who does comedy. But who wants to do other things as well."

It took her a long time to get here. After growing up in upstate New York, she went to university in Arizona and studied art before dropping out after the first year and going to LA to try to make it as an actor. Arizona is a notorious party college, but Wiig says all of that was out of her system by the time she left high school, where she had a few shaky years. "I was not that good a student because I was very… social. I cared more about going out with my friends. I didn't quite realise the importance of school. But then when I went to college I took it much more seriously, because I enjoyed it."

How social was she? Suspended?

"Um. Not for more than a couple of days. There were suspensions." Her expression fixes. "That's the past." Before the spotlight was so firmly on her, Wiig talked publicly about her minor-league acts of teenage hooliganism, including being caught underage drinking at a Grateful Deadgig, skipping school and, what she called the worst of it, smashing pot plants on a neighbour's porch, which she feels terrible about. As she entered her 20s her parents were still worried, she says, and then when she kicked in her degree and told them she wanted to be an actor, "probably the most worried they could be".

"Yes. Also, they didn't want me to get disappointed. They would always mention the numbers – do you know how many people are trying to do what you're doing? Your chances are really slim. And they're right. Technically. But when you're 20, you're like, why can't you just support me?! Can't you be proud that I'm trying to go after my dream?" She pulls a whiny face and tilts her head. "But they came around quickly when they saw how happy it made me. They would come and see me in the horrible little shows that I was in."

Wiig hadn't any great sense of being funny when she was growing up. Her dad, she says, tells a lot of jokes. Her mother is funny, but "mom funny, where she isn't trying to be funny, but is". Before retiring, her father ran a marina on one of the lakes upstate in New York (the name Wiig is from his Norwegian heritage). Her mother was an artist. Even after all these years, they haven't quite shed the sense of precariousness around their daughter's life; when she tells them she's in a movie, her mother will say tentatively, "Is that something we can see in theatres?" Wiig smiles and says, "They're still getting used to the idea that I'm working and it's OK."

With good reason. Wiig was 11 years in LA before she got the call from Saturday Night Live, during which time her income was erratic. She had arrived in the city with no professional contacts and a nagging sense of insurmountable competition. "I was incredibly intimidated and had no experience. I felt very scared and unsure and I didn't have any résumé, and everyone around me was very beautiful and young and I thought, oh, maybe I should work in a store and enjoy the weather. But I started taking improv classes and that's what got me started."

Improv was something she had never heard of before. But when she turned up to watch a gig one day at the Groundlings, the famous LA improv troupe with alumni such as Lisa Kudrow, Conan O'Brienand Will Ferrell, something resonated. The idea of standing on stage and making up stuff was, she says, less scary to her than the notion of saying lines, with the lurking fear there was a right and a wrong way to say them. With improvisation, there was no right and wrong: "You can't mess it up and you can't forget your lines."

Her enthusiasm wouldn't pay the bills, however, and Wiig worked at a series of day jobs, including at a floral design studio for a couple of years, and as a waitress in the refectory at Universal Studios. Now and then she'll run into someone on a TV show or a movie, and wonder where she knows them from. "And then I'll remember: oh yeah, I used to serve you Cobb salad."

There were many long, dark nights of the soul. "Oh my God, every month, yeah, because you don't have a lot of money coming in. When I look back, it was one of the best times of my life, because you're so in it with your friends. But you do have those moments when you're like: have I given it a try, should I stop, should I quit? But, no. You have a family there, you have a space to put shows on. I would rather be doing what I love and living above a garage – which I did – than not."

The call came in 2005. Wiig flew to New York for the first of several auditions with the Saturday Night Live creators. The audition format was standup, which she had never done before, and in front of a terrifying panel includingLorne Michaels, the legendary SNL producer, and Tina Fey. Wiig was required to unveil a range of characters of her own creation that might be suitable for the sketch show and, quivering up there alone on stage, she fully expected to be met with silence. When she heard a few laughs, she gathered strength, got through it and was called back for a second audition. After which, nothing. And then the new season started. "So I thought, right, pretty clear – thanks for coming. And then after the third show I got a call saying I was hired, come in…"

Wiig joined the show at a time when it was undergoing a cultural transition. Fey was the first female head writer and has written about the formally macho culture of the show – men pissing in jars by their desks, etc, which she put to comic use in 30 Rock. It was tough, she says, walking into a workplace where everyone knew each other: "Kind of like going into someone's living room for a party and they are really comfortable and have their shoes off and are sitting on the couch and I walk in and am a little dressed up and don't know where to stand? They were all very welcoming and nice but I knew I wasn't at that place yet where I could take my shoes off."

She was excited to be working with the likes of Fey, Amy Poehlerand Rachel Dratch, although Wiig is reluctant to describe the still testosterone-heavy environment at SNL as off-putting. "I mean, I mean, merely by numbers there are more men that work there, but I don't consider it… I don't even think about it. Men work there, women work there, we have a lot of amazing female writers on staff right now… There are more men, but I don't think anyone really…"

Was she a fan of Fey's before she joined the show?

"Um. I've watched the show since I was born. I mean I definitely admire all the stuff that she's accomplished, especially coming from SNL and being head writer, and then doing 30 Rock and all these movies and her book, I mean it's definitely something where you go, oh, that can happen. Someone can do that. She's done it. She deserves it."

To date, Bridesmaids has earned in the region of $286m worldwide; it doesn't need the qualifier "best female comedy" since it outgrossed Apatow's entire back catalogue, including Anchorman and The 40-Year-Old Virgin. Still, Wiig does not claim feminist dividends for the film – that it allowed women actors to be as gross on screen as men. She says when she and Mumolo were writing the shitting-in-the-street scene ("Can that be the title of the piece?"), it wasn't with an eye on levelling the playing field, nor was there much discussion of whether the market would tolerate that kind of vulgarity from women. No. "I think when you are doing anything creative and you think, 'What are the critics going to think?' instead of what you want to express, it can get a little muddy, and – I'm talking so seriously about this shitting-in-the-street – but with that in particular we were like, oh, this is a fun way to end the scene, and Annie used to do an impression of someone slowly realising they were shitting their pants, kind of slowly going down on to the ground. She would just do it as a joke, and it would always make me laugh really hard. She took it to a whole new level."

Apatow had approached Wiig and asked her to write a script for him after they worked together on Knocked Up, in which she played a small pivotal role as Katherine Heigl's bitchy boss. In her five minutes on screen, Wiig managed to communicate brilliantly the gap between what her character was saying and thinking. She and Mumolo first conceived of Bridesmaids not as a wedding movie per se, but as a movie about friendship. "I mean, it's called Bridesmaids, I get that. But it's about women who, when they reach that age, whether it's in their 30s or not, thought they were supposed to be somewhere else. That's where we started from. And the fact that Annie had been to seven weddings in two years. And that she had friends who were marrying money and she'd showed up at the country club for the bridal shower with her wing mirrors duct-taped to her car, and at the end of the night had to crawl through her window because the front door would always swell when it was hot out. But if it's your best friend, you don't want to be complaining…"

On paper at least, it didn't look too promising, with the generic title and the number of lame wedding movies in a seemingly exhausted genre. Apatow's name raised suspicions, too, about the use to which certain characters would be put, especially that of Megan, played by Melissa McCarthy, who looked like the inevitable one-fat-girl-in-the-group and the obvious butt of fat-girl jokes. In fact, McCarthy is the other break-out star of the film, and "the character that didn't care what anybody else thought. It was a lesson my character needed to learn. She doesn't care what anyone thinks, she's in her own world, but is generous and sweet. We wanted to have that opposite look on life, the character who seems at first like there was nothing she could say that would help, but…"

The writing of the dialogue was relatively easy, says Wiig, compared with figuring out what should happen in each scene, and the film went through countless draft versions, crammed in around other work commitments, so that Mumolo, for example, would fly out to Mexico where Wiig was filming, to work on it for a weekend. In early drafts, the women ended up in Vegas, but that got chucked out when, over the four years of writing, it was used up in other wedding films such as The Hangover.

Apart from the fact that it is very funny, Bridesmaids ultimately works because it has a kind of sweet sincerity and the friendship between the two lead characters seems real. It bemuses Wiig that the film has widely been described as "raunchy". It's really not raunchy. "Raunchy means like Porky's," she says and smiles. "Which is my next movie; it's going to be a Porky's prequel."

After six years in New York, Wiig is finally at home in the city. It was tough in the early days, she says, and when friends came to visit she would burst into tears as they left. ("I was so embarrassed. I thought, oh my God, they're going to go back and say, 'Kristen's not good. She is noooot coping well.'") If accounts are to be believed, she was briefly married to an actor called Hayes Hargrove and currently lives with her partner, a film-maker called Brian Petsos, but she responds to even the mildest question about her domestic life with a frozen smile. She would, of course, rather talk about acting, and her success in her first lead role – "I felt like I had to do a good job or no one would ever invite me to the party again" – has, despite her scrupulous modesty, been rewarded with the kind of films she always hoped she'd walk into. In the Sean Penn film The Comedian, which is still in the early stages of production, Wiig will co-star with Robert De Niro. It will be the real test of whether she is leading lady material, and whether she can carry a film without jokes. "I don't really think about it," says Wiig. "When you're in it, you're in it."

In the meantime, she has sketches to write and shoot as part of the gruelling schedule of Saturday Night Live. After the interview, she is due in at the office for the weekly writing night, when everyone is required to be in at 4pm and stay until the following morning. Wiig is riding so high at the moment that when, as we leave, I ask her to confirm her age, I'm surprised when she grimaces. Yes, she says, she's 38. Why the face? Under her breath, like a dangerous heresy, she says, "I feel like women are asked their age more than men." And she snaps on a smile and leaves the restaurant.